Simplify the following expression: $k = \dfrac{-48x - 8}{8x - 64}$ You can assume $x \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-48x - 8 = - (2\cdot2\cdot2\cdot2\cdot3 \cdot x) - (2\cdot2\cdot2)$ The denominator can be factored: $8x - 64 = (2\cdot2\cdot2 \cdot x) - (2\cdot2\cdot2\cdot2\cdot2\cdot2)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $k = \dfrac{(8)(-6x - 1)}{(8)(x - 8)}$ Dividing both the numerator and denominator by $8$ gives: $k = \dfrac{-6x - 1}{x - 8}$